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Block #928,648

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/9/2015, 6:15:02 AM Β· Difficulty 10.9037 Β· 5,880,626 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b5ccc3229e7082722f8d1cfb18e6447a5cc91e625d6803af545c43f6b30119a2
View on Chainz β†—

Height

#928,648

Difficulty

10.903663

Transactions

2

Size

364 B

Version

2

Bits

0ae75672

Nonce

660,059,197

Timestamp

2/9/2015, 6:15:02 AM

Confirmations

5,880,626

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

22ce583a41008c6ed07b27cfd0cc247d7357506bbb5b82e7faab3152c1afe3dd
Transactions (2)
Coinbase162a1f35c3b071…7659898b255748
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
879b1e4e433ea0…879cafa24f1644
1 in β†’ 1 out8.3800 XPM157 B
AekLq4Sw…ueWMfyir
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.

6.186 Γ— 10⁹⁷(98-digit number)
61866452897903164801…89465247832546017279
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
6.186 Γ— 10⁹⁷(98-digit number)
61866452897903164801…89465247832546017279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.186 Γ— 10⁹⁷(98-digit number)
61866452897903164801…89465247832546017281
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
1.237 Γ— 10⁹⁸(99-digit number)
12373290579580632960…78930495665092034559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.237 Γ— 10⁹⁸(99-digit number)
12373290579580632960…78930495665092034561
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
2.474 Γ— 10⁹⁸(99-digit number)
24746581159161265920…57860991330184069119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.474 Γ— 10⁹⁸(99-digit number)
24746581159161265920…57860991330184069121
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
4.949 Γ— 10⁹⁸(99-digit number)
49493162318322531841…15721982660368138239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.949 Γ— 10⁹⁸(99-digit number)
49493162318322531841…15721982660368138241
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
9.898 Γ— 10⁹⁸(99-digit number)
98986324636645063682…31443965320736276479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.898 Γ— 10⁹⁸(99-digit number)
98986324636645063682…31443965320736276481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,718,260 XPMΒ·at block #6,809,273 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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