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Block #1,183,936

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2015, 8:23:45 PM Β· Difficulty 10.9023 Β· 5,620,997 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
2c0e844ed971d273dfea036ca1bdabe94f6cab29d6ebe72dd6f02f3d1053e8d8
View on Chainz β†—

Height

#1,183,936

Difficulty

10.902284

Transactions

1

Size

199 B

Version

2

Bits

0ae6fc10

Nonce

902,601,902

Timestamp

8/5/2015, 8:23:45 PM

Confirmations

5,620,997

Mined by

⛏️ P2SHATsTbkknfvNb2SitDGAhDGVsVssbmFbPvm

Merkle Root

405fdff34c9aec0ccec2f77983a0dee32170fb24c6ccf051d74f4dd7030bb76f
Transactions (1)
Coinbase405fdff34c9aec…4f4dd7030bb76f
1 in β†’ 1 out8.4000 XPM109 B
ATsTbkkn…sbmFbPvm
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.

1.650 Γ— 10⁹⁡(96-digit number)
16506046214834700795…67799611998435770561
Discovered Prime Numbers
p_k = 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.

1
origin + 1
1.650 Γ— 10⁹⁡(96-digit number)
16506046214834700795…67799611998435770561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.301 Γ— 10⁹⁡(96-digit number)
33012092429669401590…35599223996871541121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.602 Γ— 10⁹⁡(96-digit number)
66024184859338803181…71198447993743082241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.320 Γ— 10⁹⁢(97-digit number)
13204836971867760636…42396895987486164481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.640 Γ— 10⁹⁢(97-digit number)
26409673943735521272…84793791974972328961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.281 Γ— 10⁹⁢(97-digit number)
52819347887471042545…69587583949944657921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.056 Γ— 10⁹⁷(98-digit number)
10563869577494208509…39175167899889315841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.112 Γ— 10⁹⁷(98-digit number)
21127739154988417018…78350335799778631681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.225 Γ— 10⁹⁷(98-digit number)
42255478309976834036…56700671599557263361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.451 Γ— 10⁹⁷(98-digit number)
84510956619953668072…13401343199114526721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.690 Γ— 10⁹⁸(99-digit number)
16902191323990733614…26802686398229053441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
3.380 Γ— 10⁹⁸(99-digit number)
33804382647981467228…53605372796458106881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,683,537 XPMΒ·at block #6,804,932 Β· updates every 60s
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