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Block #919,482

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/2/2015, 5:24:04 AM Β· Difficulty 10.9202 Β· 5,876,652 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1114fd3c22e7b72b19bb356bc89498bcb52bc523bd309d1ddc2489e67faf0dac
View on Chainz β†—

Height

#919,482

Difficulty

10.920201

Transactions

2

Size

2.12 KB

Version

2

Bits

0aeb9253

Nonce

331,076,810

Timestamp

2/2/2015, 5:24:04 AM

Confirmations

5,876,652

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2e9f7c015d62754ab57f9629b53d1ac120da3aafe251ae0ad15335aef38f5622
Transactions (2)
Coinbase9cd8fcdbe26c52…de4aa2c0af546f
1 in β†’ 1 out8.4000 XPM116 B
ANSXnLY2…Sd25TjkD
ce83ad2509a143…d32510c0e0d3ee
13 in β†’ 1 out611.5808 XPM1.92 KB
AQSTJc1q…Db5ekdjR
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.

6.530 Γ— 10⁹⁢(97-digit number)
65304512564808326360…24123734229709527039
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
6.530 Γ— 10⁹⁢(97-digit number)
65304512564808326360…24123734229709527039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.530 Γ— 10⁹⁢(97-digit number)
65304512564808326360…24123734229709527041
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
1.306 Γ— 10⁹⁷(98-digit number)
13060902512961665272…48247468459419054079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.306 Γ— 10⁹⁷(98-digit number)
13060902512961665272…48247468459419054081
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
2.612 Γ— 10⁹⁷(98-digit number)
26121805025923330544…96494936918838108159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.612 Γ— 10⁹⁷(98-digit number)
26121805025923330544…96494936918838108161
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
5.224 Γ— 10⁹⁷(98-digit number)
52243610051846661088…92989873837676216319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.224 Γ— 10⁹⁷(98-digit number)
52243610051846661088…92989873837676216321
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
1.044 Γ— 10⁹⁸(99-digit number)
10448722010369332217…85979747675352432639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.044 Γ— 10⁹⁸(99-digit number)
10448722010369332217…85979747675352432641
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:57,613,068 XPMΒ·at block #6,796,133 Β· updates every 60s
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