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Block #1,289,685

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/20/2015, 9:18:19 AM Β· Difficulty 10.8251 Β· 5,518,993 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1c5f47f3fd14db9e778935fd5168f534d44f187817237293ce66e8e4e6352236
View on Chainz β†—

Height

#1,289,685

Difficulty

10.825078

Transactions

2

Size

1.68 KB

Version

2

Bits

0ad33850

Nonce

479,826,153

Timestamp

10/20/2015, 9:18:19 AM

Confirmations

5,518,993

Mined by

⛏️ P2SHARmr3Luo81s3TPqrgDADAEyFtvGPJRZsmR

Merkle Root

81a1e0bda077a35aec3401e85c75665b9606c699a4bbe7fafc4aa675846e11d5
Transactions (2)
Coinbased5279bf508ebfb…c6c604c72f16f7
1 in β†’ 1 out8.5500 XPM110 B
ARmr3Luo…GPJRZsmR
999d9c1d9191b1…ff4207aa93312d
10 in β†’ 1 out140.3297 XPM1.49 KB
AVT53RpB…qzot2yt6
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.

2.721 Γ— 10⁹⁢(97-digit number)
27210857949021514103…00353764057261352959
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
2.721 Γ— 10⁹⁢(97-digit number)
27210857949021514103…00353764057261352959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.721 Γ— 10⁹⁢(97-digit number)
27210857949021514103…00353764057261352961
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
5.442 Γ— 10⁹⁢(97-digit number)
54421715898043028206…00707528114522705919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.442 Γ— 10⁹⁢(97-digit number)
54421715898043028206…00707528114522705921
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
1.088 Γ— 10⁹⁷(98-digit number)
10884343179608605641…01415056229045411839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10884343179608605641…01415056229045411841
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
2.176 Γ— 10⁹⁷(98-digit number)
21768686359217211282…02830112458090823679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.176 Γ— 10⁹⁷(98-digit number)
21768686359217211282…02830112458090823681
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
4.353 Γ— 10⁹⁷(98-digit number)
43537372718434422564…05660224916181647359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.353 Γ— 10⁹⁷(98-digit number)
43537372718434422564…05660224916181647361
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:57,713,470 XPMΒ·at block #6,808,677 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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