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Block #2,749,302

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/15/2018, 1:01:06 AM Β· Difficulty 11.6478 Β· 4,091,725 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d29501d5da7fbf9c5a9e9362f801f8cb338c4be055badc4a5a4fd7b8fbe5186
View on Chainz β†—

Height

#2,749,302

Difficulty

11.647756

Transactions

1

Size

200 B

Version

2

Bits

0ba5d34f

Nonce

284,680,278

Timestamp

7/15/2018, 1:01:06 AM

Confirmations

4,091,725

Mined by

⛏️ P2SHAUb7nHW661duTLkJhwyeaz2S584B9ehRgw

Merkle Root

1806c04844b925c1a0c408e25b6379192f8e3d3eee5391f946ba670884704314
Transactions (1)
Coinbase1806c04844b925…ba670884704314
1 in β†’ 1 out7.3600 XPM109 B
AUb7nHW6…4B9ehRgw
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.

1.057 Γ— 10⁹⁷(98-digit number)
10576922983283295335…00568337678628003839
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
1.057 Γ— 10⁹⁷(98-digit number)
10576922983283295335…00568337678628003839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.057 Γ— 10⁹⁷(98-digit number)
10576922983283295335…00568337678628003841
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
2.115 Γ— 10⁹⁷(98-digit number)
21153845966566590670…01136675357256007679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.115 Γ— 10⁹⁷(98-digit number)
21153845966566590670…01136675357256007681
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
4.230 Γ— 10⁹⁷(98-digit number)
42307691933133181340…02273350714512015359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.230 Γ— 10⁹⁷(98-digit number)
42307691933133181340…02273350714512015361
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
8.461 Γ— 10⁹⁷(98-digit number)
84615383866266362680…04546701429024030719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.461 Γ— 10⁹⁷(98-digit number)
84615383866266362680…04546701429024030721
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
1.692 Γ— 10⁹⁸(99-digit number)
16923076773253272536…09093402858048061439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.692 Γ— 10⁹⁸(99-digit number)
16923076773253272536…09093402858048061441
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
3.384 Γ— 10⁹⁸(99-digit number)
33846153546506545072…18186805716096122879
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:57,972,574 XPMΒ·at block #6,841,026 Β· updates every 60s
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