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Block #2,243,609

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2017, 7:34:34 AM Β· Difficulty 10.9474 Β· 4,596,065 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d497194f24d735ede68c7f85a5f97af0989514ad4d23256090a7e0b9526ce3e
View on Chainz β†—

Height

#2,243,609

Difficulty

10.947397

Transactions

2

Size

873 B

Version

2

Bits

0af2889e

Nonce

79,076,318

Timestamp

8/9/2017, 7:34:34 AM

Confirmations

4,596,065

Mined by

⛏️ P2SHAKos4pV9bp1h71i4Bw6eYuY7zeEmUaDDvy

Merkle Root

b5678b3587551961010ba7079c258b5e0e416c62949d88efcdef6c4939861b3c
Transactions (2)
Coinbase1880a78f72265d…bed2608e8a9eb1
1 in β†’ 1 out8.3400 XPM110 B
AKos4pV9…EmUaDDvy
a501ff608ffe5f…aba28a0046c6c3
4 in β†’ 2 out631.6937 XPM672 B
Abe5sdS8…sgj4hG1gAWRDnK93…19Vviqfz
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.

8.942 Γ— 10⁹⁷(98-digit number)
89422380459407553255…71468109956645683199
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
8.942 Γ— 10⁹⁷(98-digit number)
89422380459407553255…71468109956645683199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.942 Γ— 10⁹⁷(98-digit number)
89422380459407553255…71468109956645683201
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
1.788 Γ— 10⁹⁸(99-digit number)
17884476091881510651…42936219913291366399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.788 Γ— 10⁹⁸(99-digit number)
17884476091881510651…42936219913291366401
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
3.576 Γ— 10⁹⁸(99-digit number)
35768952183763021302…85872439826582732799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.576 Γ— 10⁹⁸(99-digit number)
35768952183763021302…85872439826582732801
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
7.153 Γ— 10⁹⁸(99-digit number)
71537904367526042604…71744879653165465599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.153 Γ— 10⁹⁸(99-digit number)
71537904367526042604…71744879653165465601
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
1.430 Γ— 10⁹⁹(100-digit number)
14307580873505208520…43489759306330931199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.430 Γ— 10⁹⁹(100-digit number)
14307580873505208520…43489759306330931201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.861 Γ— 10⁹⁹(100-digit number)
28615161747010417041…86979518612661862399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,961,681 XPMΒ·at block #6,839,673 Β· updates every 60s
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