Block #614,969

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/3/2014, 7:19:20 PM · Difficulty 10.9388 · 6,179,219 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7a75e6886cd56324c6b974cf88b530f505763c0f22a9703efe94dd89e4052bd

View on Chainz ↗

Height

#614,969

Difficulty

10.938792

Transactions

Size

433 B

Version

Bits

0af054a9

Nonce

13,964,379

Timestamp

7/3/2014, 7:19:20 PM

Confirmations

6,179,219

Merkle Root

7806995f2373dd6b6e59482738eda581a55fb7ab81b5204408196b5d92f4d0f4

Transactions (2)

Coinbase48e19d138931cf…72bee6f88c5d6d

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

ec2d27ead73157…af73b044783d83

1 in → 2 out5.3011 XPM225 B

AGzX6zrq…2sUqUFQZ AWFmebZg…thF7kFWh

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.318 × 10¹⁰⁰(101-digit number)

33187328831496448022…01863433763026943999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.318 × 10¹⁰⁰(101-digit number)

33187328831496448022…01863433763026943999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.318 × 10¹⁰⁰(101-digit number)

33187328831496448022…01863433763026944001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

6.637 × 10¹⁰⁰(101-digit number)

66374657662992896045…03726867526053887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.637 × 10¹⁰⁰(101-digit number)

66374657662992896045…03726867526053888001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.327 × 10¹⁰¹(102-digit number)

13274931532598579209…07453735052107775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.327 × 10¹⁰¹(102-digit number)

13274931532598579209…07453735052107776001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.654 × 10¹⁰¹(102-digit number)

26549863065197158418…14907470104215551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.654 × 10¹⁰¹(102-digit number)

26549863065197158418…14907470104215552001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.309 × 10¹⁰¹(102-digit number)

53099726130394316836…29814940208431103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.309 × 10¹⁰¹(102-digit number)

53099726130394316836…29814940208431104001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer