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Block #1,371,648

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 3:33:16 PM Β· Difficulty 10.8108 Β· 5,466,571 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
62c6f68a3ae5248e5436838e461b6e1d8d4bae1715706f1894ea150475fae156
View on Chainz β†—

Height

#1,371,648

Difficulty

10.810774

Transactions

1

Size

199 B

Version

2

Bits

0acf8ee1

Nonce

404,655,770

Timestamp

12/16/2015, 3:33:16 PM

Confirmations

5,466,571

Mined by

⛏️ P2SHAHcehCtJ8uYqgygcunixiFcgZ5qYz5qGtZ

Merkle Root

50d3d4feb5dead482ab9e9f5ead26d35cc3710662a318822f9103896629b48d3
Transactions (1)
Coinbase50d3d4feb5dead…103896629b48d3
1 in β†’ 1 out8.5400 XPM109 B
AHcehCtJ…qYz5qGtZ
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.

4.436 Γ— 10⁹⁴(95-digit number)
44363901004605819966…62667591642028007679
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
4.436 Γ— 10⁹⁴(95-digit number)
44363901004605819966…62667591642028007679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.436 Γ— 10⁹⁴(95-digit number)
44363901004605819966…62667591642028007681
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
8.872 Γ— 10⁹⁴(95-digit number)
88727802009211639932…25335183284056015359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.872 Γ— 10⁹⁴(95-digit number)
88727802009211639932…25335183284056015361
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
1.774 Γ— 10⁹⁡(96-digit number)
17745560401842327986…50670366568112030719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.774 Γ— 10⁹⁡(96-digit number)
17745560401842327986…50670366568112030721
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
3.549 Γ— 10⁹⁡(96-digit number)
35491120803684655973…01340733136224061439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.549 Γ— 10⁹⁡(96-digit number)
35491120803684655973…01340733136224061441
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
7.098 Γ— 10⁹⁡(96-digit number)
70982241607369311946…02681466272448122879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.098 Γ— 10⁹⁡(96-digit number)
70982241607369311946…02681466272448122881
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:57,950,027 XPMΒ·at block #6,838,218 Β· updates every 60s
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