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Block #2,617,861

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/17/2018, 10:59:43 AM Β· Difficulty 11.2299 Β· 4,190,522 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
bba63174e829d862b299a4c41d0a5e6ba78a656cb64b7ea38fd36b6708a8ebe0
View on Chainz β†—

Height

#2,617,861

Difficulty

11.229859

Transactions

2

Size

94.07 KB

Version

2

Bits

0b3ad810

Nonce

1,142,810,328

Timestamp

4/17/2018, 10:59:43 AM

Confirmations

4,190,522

Mined by

⛏️ P2SHAbUrWr7siWGAWeH52LmWxuPWxiChz8SyK5

Merkle Root

38a9e02fc9d4e8282d07236ff88b59a65ca312ce5ce967401505f0363bf81a6d
Transactions (2)
Coinbase9d1c64fa8afb37…0849fe84502996
1 in β†’ 1 out8.8900 XPM109 B
AbUrWr7s…Chz8SyK5
e8e7925279f8c8…31278ba76d5a7b
649 in β†’ 2 out650.0100 XPM93.88 KB
ALPF8J52…Hjw4BMsGASwBuyje…UP2qqtcm
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.224 Γ— 10⁹⁸(99-digit number)
12240321078772101980…97469926469302640639
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.224 Γ— 10⁹⁸(99-digit number)
12240321078772101980…97469926469302640639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.224 Γ— 10⁹⁸(99-digit number)
12240321078772101980…97469926469302640641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.448 Γ— 10⁹⁸(99-digit number)
24480642157544203960…94939852938605281279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.448 Γ— 10⁹⁸(99-digit number)
24480642157544203960…94939852938605281281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.896 Γ— 10⁹⁸(99-digit number)
48961284315088407920…89879705877210562559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.896 Γ— 10⁹⁸(99-digit number)
48961284315088407920…89879705877210562561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
9.792 Γ— 10⁹⁸(99-digit number)
97922568630176815841…79759411754421125119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.792 Γ— 10⁹⁸(99-digit number)
97922568630176815841…79759411754421125121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.958 Γ— 10⁹⁹(100-digit number)
19584513726035363168…59518823508842250239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.958 Γ— 10⁹⁹(100-digit number)
19584513726035363168…59518823508842250241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.916 Γ— 10⁹⁹(100-digit number)
39169027452070726336…19037647017684500479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,711,118 XPMΒ·at block #6,808,382 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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