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Block #2,152,487

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/9/2017, 1:31:57 AM Β· Difficulty 10.9018 Β· 4,689,976 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
528484440aad53330ed616732ef74d469bfc9ad6412df17bfc2cb0ba065c45ba
View on Chainz β†—

Height

#2,152,487

Difficulty

10.901768

Transactions

2

Size

424 B

Version

2

Bits

0ae6da49

Nonce

136,104,625

Timestamp

6/9/2017, 1:31:57 AM

Confirmations

4,689,976

Mined by

⛏️ P2SHAPZWhNEsAafXDjvdoAa64YTZSwuxHgtTKr

Merkle Root

5157d539a24b3d961ff985f4172fc776d9965ea3954358095af44d6df90232ba
Transactions (2)
Coinbase6e571192613777…652f95047eb7ed
1 in β†’ 1 out8.4100 XPM109 B
APZWhNEs…uxHgtTKr
9eeedbe03756f2…3ddaa38b1fb3d6
1 in β†’ 2 out9999.9900 XPM225 B
AR9T9jS6…JT8rjadFAV6GVuy1…YKkdVbyz
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.

1.180 Γ— 10⁹⁡(96-digit number)
11800698577940217917…87815693306818740719
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
1.180 Γ— 10⁹⁡(96-digit number)
11800698577940217917…87815693306818740719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.180 Γ— 10⁹⁡(96-digit number)
11800698577940217917…87815693306818740721
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
2.360 Γ— 10⁹⁡(96-digit number)
23601397155880435835…75631386613637481439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.360 Γ— 10⁹⁡(96-digit number)
23601397155880435835…75631386613637481441
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
4.720 Γ— 10⁹⁡(96-digit number)
47202794311760871670…51262773227274962879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.720 Γ— 10⁹⁡(96-digit number)
47202794311760871670…51262773227274962881
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
9.440 Γ— 10⁹⁡(96-digit number)
94405588623521743341…02525546454549925759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.440 Γ— 10⁹⁡(96-digit number)
94405588623521743341…02525546454549925761
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
1.888 Γ— 10⁹⁢(97-digit number)
18881117724704348668…05051092909099851519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.888 Γ— 10⁹⁢(97-digit number)
18881117724704348668…05051092909099851521
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
3.776 Γ— 10⁹⁢(97-digit number)
37762235449408697336…10102185818199703039
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:57,984,122 XPMΒ·at block #6,842,462 Β· updates every 60s
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