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Block #2,271,857

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 12:32:28 PM Β· Difficulty 10.9540 Β· 4,560,552 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e36e81498dd8041b25ec1907c9c3b92239a59c3d39743645c388cd9d9f65481b
View on Chainz β†—

Height

#2,271,857

Difficulty

10.954026

Transactions

2

Size

428 B

Version

2

Bits

0af43b09

Nonce

1,934,376,691

Timestamp

8/28/2017, 12:32:28 PM

Confirmations

4,560,552

Mined by

⛏️ P2SHAJwXKzT1epAJTfE84LcNcnCfyXE8hp6jat

Merkle Root

cb53237916df66bb5eb0403d233e770e3ecb7319cb90d22c61afab78a27359c7
Transactions (2)
Coinbaseb050b26e2ff11e…4bdc2ea7c31fd1
1 in β†’ 1 out8.3300 XPM110 B
AJwXKzT1…E8hp6jat
54840c7f994512…0a98998a71b638
1 in β†’ 2 out188.6246 XPM226 B
AQe8XhtH…Y8TKvtJbAdGS5NBZ…v4fsPMsA
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.

3.405 Γ— 10⁹⁸(99-digit number)
34056045362176182486…61937678819316858879
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
3.405 Γ— 10⁹⁸(99-digit number)
34056045362176182486…61937678819316858879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.405 Γ— 10⁹⁸(99-digit number)
34056045362176182486…61937678819316858881
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
6.811 Γ— 10⁹⁸(99-digit number)
68112090724352364973…23875357638633717759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.811 Γ— 10⁹⁸(99-digit number)
68112090724352364973…23875357638633717761
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
1.362 Γ— 10⁹⁹(100-digit number)
13622418144870472994…47750715277267435519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.362 Γ— 10⁹⁹(100-digit number)
13622418144870472994…47750715277267435521
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
2.724 Γ— 10⁹⁹(100-digit number)
27244836289740945989…95501430554534871039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.724 Γ— 10⁹⁹(100-digit number)
27244836289740945989…95501430554534871041
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
5.448 Γ— 10⁹⁹(100-digit number)
54489672579481891978…91002861109069742079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.448 Γ— 10⁹⁹(100-digit number)
54489672579481891978…91002861109069742081
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:57,903,417 XPMΒ·at block #6,832,408 Β· updates every 60s
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