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Block #3,106,196

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/23/2019, 5:05:33 AM Β· Difficulty 11.2205 Β· 3,736,700 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6c1e2bee5793053052e320605cabe2551a132848edc8213ea4e2f9f78d56db8d
View on Chainz β†—

Height

#3,106,196

Difficulty

11.220466

Transactions

1

Size

199 B

Version

2

Bits

0b387079

Nonce

234,386,988

Timestamp

3/23/2019, 5:05:33 AM

Confirmations

3,736,700

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

beca8fa7a60b317a727bcabde382c0e946c799cf7a623f2b5ecc36f667fd01e6
Transactions (1)
Coinbasebeca8fa7a60b31…cc36f667fd01e6
1 in β†’ 1 out7.9300 XPM110 B
AbXwmGxD…4XXYP765
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.

5.407 Γ— 10⁹¹(92-digit number)
54073462088343204331…78602982327710615239
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
5.407 Γ— 10⁹¹(92-digit number)
54073462088343204331…78602982327710615239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.407 Γ— 10⁹¹(92-digit number)
54073462088343204331…78602982327710615241
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
1.081 Γ— 10⁹²(93-digit number)
10814692417668640866…57205964655421230479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.081 Γ— 10⁹²(93-digit number)
10814692417668640866…57205964655421230481
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
2.162 Γ— 10⁹²(93-digit number)
21629384835337281732…14411929310842460959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.162 Γ— 10⁹²(93-digit number)
21629384835337281732…14411929310842460961
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
4.325 Γ— 10⁹²(93-digit number)
43258769670674563465…28823858621684921919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.325 Γ— 10⁹²(93-digit number)
43258769670674563465…28823858621684921921
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
8.651 Γ— 10⁹²(93-digit number)
86517539341349126930…57647717243369843839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.651 Γ— 10⁹²(93-digit number)
86517539341349126930…57647717243369843841
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
1.730 Γ— 10⁹³(94-digit number)
17303507868269825386…15295434486739687679
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:57,987,516 XPMΒ·at block #6,842,895 Β· updates every 60s
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