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Block #918,398

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/1/2015, 9:16:40 AM Β· Difficulty 10.9221 Β· 5,906,124 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b73e1a1c845bdd9a6f34b01181678a131ac4c0ca757747344736c2e81480e43e
View on Chainz β†—

Height

#918,398

Difficulty

10.922086

Transactions

2

Size

434 B

Version

2

Bits

0aec0dd9

Nonce

832,605,468

Timestamp

2/1/2015, 9:16:40 AM

Confirmations

5,906,124

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

34052156305cd5b5b2beaf62e1d815bb955aa128e752faad6459f2fead67473f
Transactions (2)
Coinbase90fe5ecd434ef7…e4dc80d01720f8
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
ec4edfdb1f2114…bb1ff358ff270d
1 in β†’ 2 out3937.7600 XPM226 B
AMzpcWQ3…FuZX5brPAJeVjfHj…6pTrdBmT
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.

1.043 Γ— 10⁹⁹(100-digit number)
10434202673853488318…47298382321973985279
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
1.043 Γ— 10⁹⁹(100-digit number)
10434202673853488318…47298382321973985279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.043 Γ— 10⁹⁹(100-digit number)
10434202673853488318…47298382321973985281
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
2.086 Γ— 10⁹⁹(100-digit number)
20868405347706976636…94596764643947970559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.086 Γ— 10⁹⁹(100-digit number)
20868405347706976636…94596764643947970561
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
4.173 Γ— 10⁹⁹(100-digit number)
41736810695413953272…89193529287895941119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.173 Γ— 10⁹⁹(100-digit number)
41736810695413953272…89193529287895941121
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
8.347 Γ— 10⁹⁹(100-digit number)
83473621390827906544…78387058575791882239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.347 Γ— 10⁹⁹(100-digit number)
83473621390827906544…78387058575791882241
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
1.669 Γ— 10¹⁰⁰(101-digit number)
16694724278165581308…56774117151583764479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.669 Γ— 10¹⁰⁰(101-digit number)
16694724278165581308…56774117151583764481
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:57,840,239 XPMΒ·at block #6,824,521 Β· updates every 60s
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