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Block #2,831,648

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 11:38:22 AM Β· Difficulty 11.7175 Β· 4,007,600 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4edfa6cdb336394605cea43bb75244ad8ec462d44e69367748e159dd069d9697
View on Chainz β†—

Height

#2,831,648

Difficulty

11.717516

Transactions

1

Size

200 B

Version

2

Bits

0bb7af1f

Nonce

667,564,502

Timestamp

9/9/2018, 11:38:22 AM

Confirmations

4,007,600

Mined by

⛏️ P2SHAWYgd97ThjeQgWoawMFU6az9JhjzNouCJW

Merkle Root

37cc6ecfd216cb97700535a8ff42debcd8742ad3daa1f51731194390a24c07dc
Transactions (1)
Coinbase37cc6ecfd216cb…194390a24c07dc
1 in β†’ 1 out7.2700 XPM110 B
AWYgd97T…jzNouCJW
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.

3.738 Γ— 10⁹³(94-digit number)
37380672557321783212…12402346381409318399
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
3.738 Γ— 10⁹³(94-digit number)
37380672557321783212…12402346381409318399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.738 Γ— 10⁹³(94-digit number)
37380672557321783212…12402346381409318401
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
7.476 Γ— 10⁹³(94-digit number)
74761345114643566425…24804692762818636799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.476 Γ— 10⁹³(94-digit number)
74761345114643566425…24804692762818636801
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
1.495 Γ— 10⁹⁴(95-digit number)
14952269022928713285…49609385525637273599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.495 Γ— 10⁹⁴(95-digit number)
14952269022928713285…49609385525637273601
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
2.990 Γ— 10⁹⁴(95-digit number)
29904538045857426570…99218771051274547199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.990 Γ— 10⁹⁴(95-digit number)
29904538045857426570…99218771051274547201
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
5.980 Γ— 10⁹⁴(95-digit number)
59809076091714853140…98437542102549094399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.980 Γ— 10⁹⁴(95-digit number)
59809076091714853140…98437542102549094401
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
1.196 Γ— 10⁹⁡(96-digit number)
11961815218342970628…96875084205098188799
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:57,958,266 XPMΒ·at block #6,839,247 Β· updates every 60s
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