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Block #3,086,737

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/10/2019, 10:22:15 AM Β· Difficulty 11.0380 Β· 3,756,214 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
131808ae233736330444c6aaeb475bb3003d224eb45be7d1c3d94c90a7ae1fff
View on Chainz β†—

Height

#3,086,737

Difficulty

11.037985

Transactions

1

Size

199 B

Version

2

Bits

0b09b965

Nonce

1,813,594,910

Timestamp

3/10/2019, 10:22:15 AM

Confirmations

3,756,214

Mined by

⛏️ 5AbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

247b9112b6b7151e5b85a713564c490d12a2629a852cd2eb1caf56551ce96b1d
Transactions (1)
Coinbase247b9112b6b715…af56551ce96b1d
1 in β†’ 1 out8.1900 XPM109 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.

9.951 Γ— 10⁹³(94-digit number)
99518962939778109170…55221933214161305599
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
9.951 Γ— 10⁹³(94-digit number)
99518962939778109170…55221933214161305599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.951 Γ— 10⁹³(94-digit number)
99518962939778109170…55221933214161305601
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
1.990 Γ— 10⁹⁴(95-digit number)
19903792587955621834…10443866428322611199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.990 Γ— 10⁹⁴(95-digit number)
19903792587955621834…10443866428322611201
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
3.980 Γ— 10⁹⁴(95-digit number)
39807585175911243668…20887732856645222399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.980 Γ— 10⁹⁴(95-digit number)
39807585175911243668…20887732856645222401
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
7.961 Γ— 10⁹⁴(95-digit number)
79615170351822487336…41775465713290444799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.961 Γ— 10⁹⁴(95-digit number)
79615170351822487336…41775465713290444801
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
1.592 Γ— 10⁹⁡(96-digit number)
15923034070364497467…83550931426580889599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.592 Γ— 10⁹⁡(96-digit number)
15923034070364497467…83550931426580889601
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
3.184 Γ— 10⁹⁡(96-digit number)
31846068140728994934…67101862853161779199
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:57,987,960 XPMΒ·at block #6,842,950 Β· updates every 60s
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