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Block #2,271,961

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 2:10:50 PM Β· Difficulty 10.9541 Β· 4,554,739 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
924bfa9999b928077d03fb9924bed130489b0c707694e42e4813d80080bf6705
View on Chainz β†—

Height

#2,271,961

Difficulty

10.954079

Transactions

2

Size

1.14 KB

Version

2

Bits

0af43e81

Nonce

1,784,254,482

Timestamp

8/28/2017, 2:10:50 PM

Confirmations

4,554,739

Mined by

⛏️ P2SHAYFjSCFtwn6JyZ3b7irhi2yRGxR7wXbw3n

Merkle Root

c0342c685cc8d959bced76aaa33368423ff3fa26b35aba53c2d6f64c73ee2e98
Transactions (2)
Coinbase9f175a20b0d30e…bed6d0beb34459
1 in β†’ 1 out8.3300 XPM109 B
AYFjSCFt…R7wXbw3n
f36e0c772302a3…0a041e8906e140
6 in β†’ 2 out2000.4417 XPM967 B
ARaNCeSx…b8M3uhxYAZy8pG7z…yb4zZxKq
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.

1.012 Γ— 10⁹⁴(95-digit number)
10126137826760680175…61218028110543441199
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
1.012 Γ— 10⁹⁴(95-digit number)
10126137826760680175…61218028110543441199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.012 Γ— 10⁹⁴(95-digit number)
10126137826760680175…61218028110543441201
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
2.025 Γ— 10⁹⁴(95-digit number)
20252275653521360351…22436056221086882399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.025 Γ— 10⁹⁴(95-digit number)
20252275653521360351…22436056221086882401
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
4.050 Γ— 10⁹⁴(95-digit number)
40504551307042720703…44872112442173764799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.050 Γ— 10⁹⁴(95-digit number)
40504551307042720703…44872112442173764801
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
8.100 Γ— 10⁹⁴(95-digit number)
81009102614085441407…89744224884347529599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.100 Γ— 10⁹⁴(95-digit number)
81009102614085441407…89744224884347529601
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
1.620 Γ— 10⁹⁡(96-digit number)
16201820522817088281…79488449768695059199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.620 Γ— 10⁹⁡(96-digit number)
16201820522817088281…79488449768695059201
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:57,857,752 XPMΒ·at block #6,826,699 Β· updates every 60s
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