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Block #1,312,370

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/4/2015, 1:38:22 PM Β· Difficulty 10.8523 Β· 5,529,137 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
43be0694246018da6d99ca27542a6345287497f9536da9b63a5bed4f4140aa33
View on Chainz β†—

Height

#1,312,370

Difficulty

10.852303

Transactions

1

Size

200 B

Version

2

Bits

0ada308a

Nonce

402,528,316

Timestamp

11/4/2015, 1:38:22 PM

Confirmations

5,529,137

Mined by

⛏️ P2SHAPzSLExWe9kJk22Amf1yoTjhvHbEzUGphs

Merkle Root

548dff2f237fe0998c057c106ccd16de0579e578b5af33f59e5edb2adedef1fc
Transactions (1)
Coinbase548dff2f237fe0…5edb2adedef1fc
1 in β†’ 1 out8.4800 XPM110 B
APzSLExW…bEzUGphs
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.

5.101 Γ— 10⁹⁡(96-digit number)
51014160118381633279…11226879468417509119
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
5.101 Γ— 10⁹⁡(96-digit number)
51014160118381633279…11226879468417509119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.101 Γ— 10⁹⁡(96-digit number)
51014160118381633279…11226879468417509121
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
1.020 Γ— 10⁹⁢(97-digit number)
10202832023676326655…22453758936835018239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.020 Γ— 10⁹⁢(97-digit number)
10202832023676326655…22453758936835018241
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
2.040 Γ— 10⁹⁢(97-digit number)
20405664047352653311…44907517873670036479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.040 Γ— 10⁹⁢(97-digit number)
20405664047352653311…44907517873670036481
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
4.081 Γ— 10⁹⁢(97-digit number)
40811328094705306623…89815035747340072959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.081 Γ— 10⁹⁢(97-digit number)
40811328094705306623…89815035747340072961
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
8.162 Γ— 10⁹⁢(97-digit number)
81622656189410613247…79630071494680145919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.162 Γ— 10⁹⁢(97-digit number)
81622656189410613247…79630071494680145921
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:57,976,435 XPMΒ·at block #6,841,506 Β· updates every 60s
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