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Block #1,932,733

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2017, 8:48:15 AM Β· Difficulty 10.7622 Β· 4,881,204 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bba6d9ba0f576bb0b9dccb12d09bf5b99a5dfdc3e65dd6ebd4d9d84a135cc846
View on Chainz β†—

Height

#1,932,733

Difficulty

10.762225

Transactions

2

Size

1.11 KB

Version

2

Bits

0ac32127

Nonce

233,536,429

Timestamp

1/10/2017, 8:48:15 AM

Confirmations

4,881,204

Mined by

⛏️ P2SHART6QN6LpqEA6pUuvPMFpTE8Dyi3gP4qX2

Merkle Root

ab4d37ac5cba38d5c7097a0a357c942e1f15df6e10e77dc954597baca596ecfb
Transactions (2)
Coinbasee04bcbef2e18dc…21ad1be0185d09
1 in β†’ 1 out8.6300 XPM110 B
ART6QN6L…i3gP4qX2
ac0f4a935cd50a…2d78f8e5e745d1
6 in β†’ 1 out754.9164 XPM934 B
ALEDfJ34…figSU7mC
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.

1.912 Γ— 10⁹³(94-digit number)
19121684304724179686…53861757989791011429
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
1.912 Γ— 10⁹³(94-digit number)
19121684304724179686…53861757989791011429
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.912 Γ— 10⁹³(94-digit number)
19121684304724179686…53861757989791011431
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
3.824 Γ— 10⁹³(94-digit number)
38243368609448359372…07723515979582022859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.824 Γ— 10⁹³(94-digit number)
38243368609448359372…07723515979582022861
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
7.648 Γ— 10⁹³(94-digit number)
76486737218896718745…15447031959164045719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.648 Γ— 10⁹³(94-digit number)
76486737218896718745…15447031959164045721
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
1.529 Γ— 10⁹⁴(95-digit number)
15297347443779343749…30894063918328091439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.529 Γ— 10⁹⁴(95-digit number)
15297347443779343749…30894063918328091441
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
3.059 Γ— 10⁹⁴(95-digit number)
30594694887558687498…61788127836656182879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.059 Γ— 10⁹⁴(95-digit number)
30594694887558687498…61788127836656182881
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:57,755,572 XPMΒ·at block #6,813,936 Β· updates every 60s
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