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Block #918,866

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/1/2015, 5:34:57 PM Β· Difficulty 10.9216 Β· 5,889,867 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
61c437dad9d3b85230bfed79119be45b3a54ea5fde69d0243347d5be4d6c1de1
View on Chainz β†—

Height

#918,866

Difficulty

10.921641

Transactions

2

Size

5.62 KB

Version

2

Bits

0aebf0aa

Nonce

817,058,443

Timestamp

2/1/2015, 5:34:57 PM

Confirmations

5,889,867

Mined by

⛏️ P2SHAKLzDdN5sQAdn7Cgmofd3EXhJDuFtFgxZG

Merkle Root

642b26d8a4f90c9987ff0e0b865a3c2d8715d6f13719c2b092f8a53686f10f2c
Transactions (2)
Coinbase4e6e6d7edae613…332f26e3b09e89
1 in β†’ 1 out8.4300 XPM110 B
AKLzDdN5…uFtFgxZG
176ff5c13c1e8c…f2704e02874fd3
37 in β†’ 2 out1838.9273 XPM5.42 KB
AcpcUK1K…DBKsbJtgAcAFW717…V1pWEX3J
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.

6.454 Γ— 10⁹³(94-digit number)
64548438157531911526…70845950889510114799
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
6.454 Γ— 10⁹³(94-digit number)
64548438157531911526…70845950889510114799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.454 Γ— 10⁹³(94-digit number)
64548438157531911526…70845950889510114801
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
1.290 Γ— 10⁹⁴(95-digit number)
12909687631506382305…41691901779020229599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.290 Γ— 10⁹⁴(95-digit number)
12909687631506382305…41691901779020229601
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
2.581 Γ— 10⁹⁴(95-digit number)
25819375263012764610…83383803558040459199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.581 Γ— 10⁹⁴(95-digit number)
25819375263012764610…83383803558040459201
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
5.163 Γ— 10⁹⁴(95-digit number)
51638750526025529221…66767607116080918399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.163 Γ— 10⁹⁴(95-digit number)
51638750526025529221…66767607116080918401
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
1.032 Γ— 10⁹⁡(96-digit number)
10327750105205105844…33535214232161836799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.032 Γ— 10⁹⁡(96-digit number)
10327750105205105844…33535214232161836801
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:57,713,910 XPMΒ·at block #6,808,732 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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