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Block #186,123

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/29/2013, 5:38:33 PM Β· Difficulty 9.8644 Β· 6,617,293 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fd42cdba5cc84cf64a641e489def277691b53e727531c4f5c9f7af0746b0196c
View on Chainz β†—

Height

#186,123

Difficulty

9.864415

Transactions

1

Size

206 B

Version

2

Bits

09dd4a4e

Nonce

33,556,033

Timestamp

9/29/2013, 5:38:33 PM

Confirmations

6,617,293

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

032932fb1cad84055818ba7de82ba09cb30f89aff9d6863fd089b897a36955e5
Transactions (1)
Coinbase032932fb1cad84…89b897a36955e5
1 in β†’ 1 out10.2600 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.532 Γ— 10⁹³(94-digit number)
55326853575937793887…93933181491012605439
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
5.532 Γ— 10⁹³(94-digit number)
55326853575937793887…93933181491012605439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.532 Γ— 10⁹³(94-digit number)
55326853575937793887…93933181491012605441
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
1.106 Γ— 10⁹⁴(95-digit number)
11065370715187558777…87866362982025210879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.106 Γ— 10⁹⁴(95-digit number)
11065370715187558777…87866362982025210881
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
2.213 Γ— 10⁹⁴(95-digit number)
22130741430375117555…75732725964050421759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.213 Γ— 10⁹⁴(95-digit number)
22130741430375117555…75732725964050421761
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
4.426 Γ— 10⁹⁴(95-digit number)
44261482860750235110…51465451928100843519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.426 Γ— 10⁹⁴(95-digit number)
44261482860750235110…51465451928100843521
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
8.852 Γ— 10⁹⁴(95-digit number)
88522965721500470220…02930903856201687039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.852 Γ— 10⁹⁴(95-digit number)
88522965721500470220…02930903856201687041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,671,359 XPMΒ·at block #6,803,415 Β· updates every 60s
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