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Block #631,506

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2014, 3:26:32 PM Β· Difficulty 10.9622 Β· 6,175,557 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
286be0a54e1c2258d7ad3af10a308553692033370a5597e119d7ccac082baee4
View on Chainz β†—

Height

#631,506

Difficulty

10.962187

Transactions

1

Size

200 B

Version

2

Bits

0af651ea

Nonce

98,816

Timestamp

7/13/2014, 3:26:32 PM

Confirmations

6,175,557

Mined by

⛏️ P2SHAHFWCKWQT8LyddsuRBgu53KwDFW7CD8T1C

Merkle Root

15795a9346f9ee6306ae97f72e10b34bedb2f754e12c68431bc888c0e3fb1aa6
Transactions (1)
Coinbase15795a9346f9ee…c888c0e3fb1aa6
1 in β†’ 1 out8.3100 XPM111 B
AHFWCKWQ…W7CD8T1C
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.

6.123 Γ— 10⁹¹(92-digit number)
61238488874376321822…39694338747786306429
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
6.123 Γ— 10⁹¹(92-digit number)
61238488874376321822…39694338747786306429
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.123 Γ— 10⁹¹(92-digit number)
61238488874376321822…39694338747786306431
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
1.224 Γ— 10⁹²(93-digit number)
12247697774875264364…79388677495572612859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.224 Γ— 10⁹²(93-digit number)
12247697774875264364…79388677495572612861
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
2.449 Γ— 10⁹²(93-digit number)
24495395549750528728…58777354991145225719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.449 Γ— 10⁹²(93-digit number)
24495395549750528728…58777354991145225721
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
4.899 Γ— 10⁹²(93-digit number)
48990791099501057457…17554709982290451439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.899 Γ— 10⁹²(93-digit number)
48990791099501057457…17554709982290451441
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
9.798 Γ— 10⁹²(93-digit number)
97981582199002114915…35109419964580902879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.798 Γ— 10⁹²(93-digit number)
97981582199002114915…35109419964580902881
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:57,700,602 XPMΒ·at block #6,807,062 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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