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Block #1,681,327

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2016, 6:56:05 AM Β· Difficulty 10.7148 Β· 5,160,464 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
71972d15a84d5619c0efeb2e95f45084e2f0dce872ec5c94d7b18e20d2d551a0
View on Chainz β†—

Height

#1,681,327

Difficulty

10.714816

Transactions

1

Size

199 B

Version

2

Bits

0ab6fe2f

Nonce

2,003,611,192

Timestamp

7/20/2016, 6:56:05 AM

Confirmations

5,160,464

Mined by

⛏️ P2SHAZ7UBx9wcaEsHVvAphkDcRrtFeEs8ve9eW

Merkle Root

2d6ee5ed6972924c0c046acccdb897ccdaad6129f47603e40f0389d6a126cef0
Transactions (1)
Coinbase2d6ee5ed697292…0389d6a126cef0
1 in β†’ 1 out8.7000 XPM109 B
AZ7UBx9w…Es8ve9eW
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.

2.224 Γ— 10⁹⁡(96-digit number)
22248280455322850687…39407651286763699839
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
2.224 Γ— 10⁹⁡(96-digit number)
22248280455322850687…39407651286763699839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.224 Γ— 10⁹⁡(96-digit number)
22248280455322850687…39407651286763699841
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
4.449 Γ— 10⁹⁡(96-digit number)
44496560910645701374…78815302573527399679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.449 Γ— 10⁹⁡(96-digit number)
44496560910645701374…78815302573527399681
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
8.899 Γ— 10⁹⁡(96-digit number)
88993121821291402749…57630605147054799359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.899 Γ— 10⁹⁡(96-digit number)
88993121821291402749…57630605147054799361
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
1.779 Γ— 10⁹⁢(97-digit number)
17798624364258280549…15261210294109598719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.779 Γ— 10⁹⁢(97-digit number)
17798624364258280549…15261210294109598721
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
3.559 Γ— 10⁹⁢(97-digit number)
35597248728516561099…30522420588219197439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.559 Γ— 10⁹⁢(97-digit number)
35597248728516561099…30522420588219197441
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:57,978,706 XPMΒ·at block #6,841,790 Β· updates every 60s
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