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Block #2,552,867

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/7/2018, 2:37:13 AM Β· Difficulty 10.9899 Β· 4,281,086 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
97356648efafa5ce1ad3c828fa70bf1a066585315cf4843d66431697fbd4df66
View on Chainz β†—

Height

#2,552,867

Difficulty

10.989900

Transactions

3

Size

47.59 KB

Version

2

Bits

0afd6a17

Nonce

1,921,422,226

Timestamp

3/7/2018, 2:37:13 AM

Confirmations

4,281,086

Mined by

⛏️ P2SHAHVuRsc6sJ6FFzxqudt2HMoS1zJwasvY28

Merkle Root

b7f2be2bbba0a7c38ae5e1a4530963c0e6dff7b18a659bc667425ed997f89711
Transactions (3)
Coinbasef64c828710075a…28828e7377f21b
1 in β†’ 1 out8.7700 XPM110 B
AHVuRsc6…JwasvY28
a0e46ff0395c56…9759aec38420d8
326 in β†’ 1 out3274.0004 XPM47.18 KB
ALPF8J52…Hjw4BMsG
f36a308cddca3c…959797250de696
1 in β†’ 2 out2.4992 XPM226 B
ANWdJ2nc…BW7RisDkALdt15pq…e88YwMRc
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.

5.108 Γ— 10⁹⁴(95-digit number)
51083564298622752519…69883403132084059839
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
5.108 Γ— 10⁹⁴(95-digit number)
51083564298622752519…69883403132084059839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.108 Γ— 10⁹⁴(95-digit number)
51083564298622752519…69883403132084059841
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
1.021 Γ— 10⁹⁡(96-digit number)
10216712859724550503…39766806264168119679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.021 Γ— 10⁹⁡(96-digit number)
10216712859724550503…39766806264168119681
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
2.043 Γ— 10⁹⁡(96-digit number)
20433425719449101007…79533612528336239359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.043 Γ— 10⁹⁡(96-digit number)
20433425719449101007…79533612528336239361
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
4.086 Γ— 10⁹⁡(96-digit number)
40866851438898202015…59067225056672478719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.086 Γ— 10⁹⁡(96-digit number)
40866851438898202015…59067225056672478721
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
8.173 Γ— 10⁹⁡(96-digit number)
81733702877796404031…18134450113344957439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.173 Γ— 10⁹⁡(96-digit number)
81733702877796404031…18134450113344957441
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
1.634 Γ— 10⁹⁢(97-digit number)
16346740575559280806…36268900226689914879
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:57,915,853 XPMΒ·at block #6,833,952 Β· updates every 60s
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