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Block #1,223,603

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2015, 7:52:08 PM Β· Difficulty 10.7414 Β· 5,580,605 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
71859bf3768741864aa92d484990418e0fae882d261b8e865153c4a9d6f58d25
View on Chainz β†—

Height

#1,223,603

Difficulty

10.741449

Transactions

1

Size

208 B

Version

2

Bits

0abdcf9f

Nonce

8,900,876

Timestamp

9/5/2015, 7:52:08 PM

Confirmations

5,580,605

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

8a1856b365ed09dc90a8e26d83d06701c6e4cbac70865c86716e0d8a783c7e48
Transactions (1)
Coinbase8a1856b365ed09…6e0d8a783c7e48
1 in β†’ 1 out8.6500 XPM116 B
AJCEY9yy…tg97E6zm
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.

3.932 Γ— 10⁹⁸(99-digit number)
39329824040278040885…23472312877585530879
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
3.932 Γ— 10⁹⁸(99-digit number)
39329824040278040885…23472312877585530879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.932 Γ— 10⁹⁸(99-digit number)
39329824040278040885…23472312877585530881
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
7.865 Γ— 10⁹⁸(99-digit number)
78659648080556081770…46944625755171061759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.865 Γ— 10⁹⁸(99-digit number)
78659648080556081770…46944625755171061761
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
1.573 Γ— 10⁹⁹(100-digit number)
15731929616111216354…93889251510342123519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.573 Γ— 10⁹⁹(100-digit number)
15731929616111216354…93889251510342123521
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
3.146 Γ— 10⁹⁹(100-digit number)
31463859232222432708…87778503020684247039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.146 Γ— 10⁹⁹(100-digit number)
31463859232222432708…87778503020684247041
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
6.292 Γ— 10⁹⁹(100-digit number)
62927718464444865416…75557006041368494079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.292 Γ— 10⁹⁹(100-digit number)
62927718464444865416…75557006041368494081
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:57,677,712 XPMΒ·at block #6,804,207 Β· updates every 60s
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