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Block #980,927

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/19/2015, 6:01:13 AM Β· Difficulty 10.8471 Β· 5,825,708 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b21c8e28f201b2cfe93338d1f7d382b30bf53ec1966d2d72d20e1febea822b71
View on Chainz β†—

Height

#980,927

Difficulty

10.847080

Transactions

2

Size

729 B

Version

2

Bits

0ad8da3a

Nonce

21,948,409

Timestamp

3/19/2015, 6:01:13 AM

Confirmations

5,825,708

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

861b6709a6d4649e11fab0557bf630eb3d8ffdb2fad523f7cda7ee0c4a4d63a2
Transactions (2)
Coinbase83e493939e7a42…fa6a8d0769e95a
1 in β†’ 1 out8.5000 XPM116 B
ANSXnLY2…Sd25TjkD
f35ce6c29081ec…877017b8bf7eb2
3 in β†’ 2 out20.3265 XPM522 B
AZtDdA9R…mdeMMVPoAWFbZZAA…8buWmWjK
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.

1.836 Γ— 10⁹⁢(97-digit number)
18363101626295893275…18719641490944110719
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
1.836 Γ— 10⁹⁢(97-digit number)
18363101626295893275…18719641490944110719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.836 Γ— 10⁹⁢(97-digit number)
18363101626295893275…18719641490944110721
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
3.672 Γ— 10⁹⁢(97-digit number)
36726203252591786550…37439282981888221439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.672 Γ— 10⁹⁢(97-digit number)
36726203252591786550…37439282981888221441
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
7.345 Γ— 10⁹⁢(97-digit number)
73452406505183573101…74878565963776442879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.345 Γ— 10⁹⁢(97-digit number)
73452406505183573101…74878565963776442881
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
1.469 Γ— 10⁹⁷(98-digit number)
14690481301036714620…49757131927552885759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.469 Γ— 10⁹⁷(98-digit number)
14690481301036714620…49757131927552885761
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
2.938 Γ— 10⁹⁷(98-digit number)
29380962602073429240…99514263855105771519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.938 Γ— 10⁹⁷(98-digit number)
29380962602073429240…99514263855105771521
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:57,697,174 XPMΒ·at block #6,806,634 Β· updates every 60s
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