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Block #2,680,527

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/27/2018, 6:42:31 PM Β· Difficulty 11.6928 Β· 4,161,817 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d2332bffabb45fbccded61fea18c04466e7dac36d3121ab3610dac1ca489f2ce
View on Chainz β†—

Height

#2,680,527

Difficulty

11.692778

Transactions

1

Size

199 B

Version

2

Bits

0bb159e9

Nonce

311,578,079

Timestamp

5/27/2018, 6:42:31 PM

Confirmations

4,161,817

Mined by

⛏️ P2SHAKon7GUqCCjX263XXP5kvhaJzdqa7uSxJL

Merkle Root

9df9694bff496cb789e45ee32cff160cc67926900ddb0a2c95eef81ed7c6721e
Transactions (1)
Coinbase9df9694bff496c…eef81ed7c6721e
1 in β†’ 1 out7.3000 XPM110 B
AKon7GUq…qa7uSxJL
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.

1.110 Γ— 10⁹³(94-digit number)
11107949694865464780…18676250013618485119
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
1.110 Γ— 10⁹³(94-digit number)
11107949694865464780…18676250013618485119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.110 Γ— 10⁹³(94-digit number)
11107949694865464780…18676250013618485121
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
2.221 Γ— 10⁹³(94-digit number)
22215899389730929561…37352500027236970239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.221 Γ— 10⁹³(94-digit number)
22215899389730929561…37352500027236970241
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
4.443 Γ— 10⁹³(94-digit number)
44431798779461859123…74705000054473940479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.443 Γ— 10⁹³(94-digit number)
44431798779461859123…74705000054473940481
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
8.886 Γ— 10⁹³(94-digit number)
88863597558923718247…49410000108947880959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.886 Γ— 10⁹³(94-digit number)
88863597558923718247…49410000108947880961
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
1.777 Γ— 10⁹⁴(95-digit number)
17772719511784743649…98820000217895761919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.777 Γ— 10⁹⁴(95-digit number)
17772719511784743649…98820000217895761921
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
3.554 Γ— 10⁹⁴(95-digit number)
35545439023569487298…97640000435791523839
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:57,983,159 XPMΒ·at block #6,842,343 Β· updates every 60s
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