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Block #1,371,833

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 6:49:00 PM Β· Difficulty 10.8104 Β· 5,471,383 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
281c9ac120089938fe03dd042c3c5170440c230d403e74dfcc0b263340431d71
View on Chainz β†—

Height

#1,371,833

Difficulty

10.810410

Transactions

1

Size

200 B

Version

2

Bits

0acf770b

Nonce

983,033,095

Timestamp

12/16/2015, 6:49:00 PM

Confirmations

5,471,383

Mined by

⛏️ P2SHARUb85cmKYjpQSJpgvEW1tufLJEa1SDknz

Merkle Root

48d925d690231fe3a7d2a92e15597ab544e9b7d58383d7b7a91c4b6329810d57
Transactions (1)
Coinbase48d925d690231f…1c4b6329810d57
1 in β†’ 1 out8.5400 XPM110 B
ARUb85cm…Ea1SDknz
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.

5.848 Γ— 10⁹⁴(95-digit number)
58486152142690269165…18044989070187134399
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
5.848 Γ— 10⁹⁴(95-digit number)
58486152142690269165…18044989070187134399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.848 Γ— 10⁹⁴(95-digit number)
58486152142690269165…18044989070187134401
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
1.169 Γ— 10⁹⁡(96-digit number)
11697230428538053833…36089978140374268799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.169 Γ— 10⁹⁡(96-digit number)
11697230428538053833…36089978140374268801
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
2.339 Γ— 10⁹⁡(96-digit number)
23394460857076107666…72179956280748537599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.339 Γ— 10⁹⁡(96-digit number)
23394460857076107666…72179956280748537601
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
4.678 Γ— 10⁹⁡(96-digit number)
46788921714152215332…44359912561497075199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.678 Γ— 10⁹⁡(96-digit number)
46788921714152215332…44359912561497075201
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
9.357 Γ— 10⁹⁡(96-digit number)
93577843428304430665…88719825122994150399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.357 Γ— 10⁹⁡(96-digit number)
93577843428304430665…88719825122994150401
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:57,990,101 XPMΒ·at block #6,843,215 Β· updates every 60s
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