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Block #574,670

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2014, 11:34:41 AM Β· Difficulty 10.9678 Β· 6,220,663 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8354269a5bd1ae95eb63de2d98e622b296399892fd24e2a69a731e91dee7666c
View on Chainz β†—

Height

#574,670

Difficulty

10.967798

Transactions

1

Size

244 B

Version

2

Bits

0af7c1a3

Nonce

482,790,439

Timestamp

6/3/2014, 11:34:41 AM

Confirmations

6,220,663

Mined by

⛏️ P2SHAXn1KW6PTFKBcGVcbZ8CPoUc4Pc7VDu2zv

Merkle Root

e1cef42eb5478c6b777352ee5abafc08fe6b07f526803bd403be6f3913093557
Transactions (1)
Coinbasee1cef42eb5478c…be6f3913093557
1 in β†’ 2 out8.3000 XPM152 B
AXn1KW6P…c7VDu2zvALPu3s2c…EJXLjVFh
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.

1.311 Γ— 10⁹⁹(100-digit number)
13113469100555355083…86001534744747822079
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
1.311 Γ— 10⁹⁹(100-digit number)
13113469100555355083…86001534744747822079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.311 Γ— 10⁹⁹(100-digit number)
13113469100555355083…86001534744747822081
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
2.622 Γ— 10⁹⁹(100-digit number)
26226938201110710166…72003069489495644159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.622 Γ— 10⁹⁹(100-digit number)
26226938201110710166…72003069489495644161
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
5.245 Γ— 10⁹⁹(100-digit number)
52453876402221420333…44006138978991288319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.245 Γ— 10⁹⁹(100-digit number)
52453876402221420333…44006138978991288321
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
1.049 Γ— 10¹⁰⁰(101-digit number)
10490775280444284066…88012277957982576639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.049 Γ— 10¹⁰⁰(101-digit number)
10490775280444284066…88012277957982576641
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
2.098 Γ— 10¹⁰⁰(101-digit number)
20981550560888568133…76024555915965153279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.098 Γ— 10¹⁰⁰(101-digit number)
20981550560888568133…76024555915965153281
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:57,606,722 XPMΒ·at block #6,795,332 Β· updates every 60s
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