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Block #2,788,748

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/11/2018, 4:23:36 AM Β· Difficulty 11.6736 Β· 4,056,557 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2c3286bb0cfc72d1c8677da10b2293fcec4871a166b1a7daa1b80ca066f0fe4
View on Chainz β†—

Height

#2,788,748

Difficulty

11.673577

Transactions

1

Size

201 B

Version

2

Bits

0bac6f84

Nonce

510,431,995

Timestamp

8/11/2018, 4:23:36 AM

Confirmations

4,056,557

Mined by

⛏️ P2SHAX1S7bXjuU8RKRM4sSba4uQf7aD6UVe4eb

Merkle Root

af0b8a5f1f4a804c863793a159cdfd41fea0cdecf95ee145fe8ce4a6d144ae5f
Transactions (1)
Coinbaseaf0b8a5f1f4a80…8ce4a6d144ae5f
1 in β†’ 1 out7.3300 XPM110 B
AX1S7bXj…D6UVe4eb
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.

3.965 Γ— 10⁹⁢(97-digit number)
39652283475167228509…04549883519022243839
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
3.965 Γ— 10⁹⁢(97-digit number)
39652283475167228509…04549883519022243839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.965 Γ— 10⁹⁢(97-digit number)
39652283475167228509…04549883519022243841
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
7.930 Γ— 10⁹⁢(97-digit number)
79304566950334457019…09099767038044487679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.930 Γ— 10⁹⁢(97-digit number)
79304566950334457019…09099767038044487681
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
1.586 Γ— 10⁹⁷(98-digit number)
15860913390066891403…18199534076088975359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.586 Γ— 10⁹⁷(98-digit number)
15860913390066891403…18199534076088975361
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
3.172 Γ— 10⁹⁷(98-digit number)
31721826780133782807…36399068152177950719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.172 Γ— 10⁹⁷(98-digit number)
31721826780133782807…36399068152177950721
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
6.344 Γ— 10⁹⁷(98-digit number)
63443653560267565615…72798136304355901439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.344 Γ— 10⁹⁷(98-digit number)
63443653560267565615…72798136304355901441
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
1.268 Γ— 10⁹⁸(99-digit number)
12688730712053513123…45596272608711802879
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:58,006,880 XPMΒ·at block #6,845,304 Β· updates every 60s
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